Q. Five digited numbers with distinct digits are formed by using the digits, 5, 4, 3, 2, 1, 0. The number of those numbers which are multiples of 3, is
A) 720
B) 240
C) 216
D) 120
Explanation
(c)
A number is divisible by 3, if the sum of the digits is divisible by 3
Since, 1+2+3+4+5=15 is divisible by 3, therefore total such numbers is $5!\ \ ie$, 120
And, other five digits whose sum is divisible by 3 are 0, 1, 2, 4, 5
Therefore, number of such formed numbers$= 5! - 4! = 96$
Hence, the required number if numbers=120+96=216
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.